In a wok over medium-high heat, heat vegan rice wine or mirin until bubbling. Add ginger, garlic, carrots and broccoli. Stir-fry until carrots soften slightly, about five minutes. Add cabbage and green onions; cover and cook three minutes. With a slotted spoon, remove vegetables to a platter and set aside.
Add water, sesame oil, up to 1 tsp. cayenne and hoisin sauce, if desired, to wok and heat until bubbling. Add noodles and stir-fry until heated through. Add vegetables and heat through. Add soy sauce to taste.
Note: The sesame oil gives this dish a great flavor, but leave it out if you can't afford the few grams of fat it contributes.